Question: Simplify the following expression: $t = \dfrac{r^2 - 5r - 24}{r + 3} $
First factor the polynomial in the numerator. $ r^2 - 5r - 24 = (r + 3)(r - 8) $ So we can rewrite the expression as: $t = \dfrac{(r + 3)(r - 8)}{r + 3} $ We can divide the numerator and denominator by $(r + 3)$ on condition that $r \neq -3$ Therefore $t = r - 8; r \neq -3$